Abstract

Discrete solitons in nonlinear lattices have lately received considerable attention in diverse branches of science. These solitons are possible in several physical settings such as, for example, biological systems, nonlinear optics, solid state physics, and Bose-Einstein condensates. In optics, discrete solitons were first predicted in nonlinear waveguide array lattices in1988 [1] and were successfully observed a decade later [2]. Optical discrete solitons (DSs) are, in general, self-trapped entities of finite extent that exist in coupled periodic nonlinear lattices. They are self-localized wavepackets whose energy resides primarily in distinct waveguide array sites (hence discrete-see Fig.1) and exist through a balance of discrete diffraction/coupling effects and material nonlinearity. Unlike their continuous counterparts, DSs represent collective excitations of the nonlinear chain, and as a result, they exhibit a host of interesting characteristics that would have been absent in the bulk. Depending on the nature of the underlying nonlinear process, different families of discrete solitons are possible. To date, arrays made from materials having intensity-dependent Kerr [2], quadratic [3], as well as photorefractive nonlinearities [4] have been shown to support such discrete localized states. Various types of DSs such as in-phase, staggered or gap, twisted, vortex etc will be discussed. Such discrete nonlinear states were first observed in one-dimensional topologies and only very recently in two-dimensional systems using optical induction techniques [4,5]. In two dimensions the system exhibits behavior that is quite different compared to the 1D case. 2D gap lattice solitons always exhibit power thresholds and exist only when the associated bandgap is complete (for a specific eigenvalue all the Bloch vectors of the reduced Brillouin zone reside in the same gap). In addition, it has been theoretically demonstrated that discrete solitons in two-dimensional nonlinear waveguide array networks can provide a rich environment for all-optical data processing applications [6]. More specifically, it has been shown that this family of solitons can be employed to realize intelligent functional operations such as routing, blocking, logic functions, time-gating etc. These DS can be navigated anywhere in the network along pre-assigned array pathways that act like “soliton wires”. In principle, discrete solitons can also exist in three-dimensional environments [6]. One such possibility may be in coupled-resonator optical waveguides (CROWs) where waveguiding is accomplished via light hopping among successive high-Q microcavities that effectively act like defects when embedded in a photonic crystal. However, unlike their spatial cousins in waveguide arrays, DSs in CROWs are by nature spatiotemporal entities. These self-localized entities are capable of exhibiting very low group velocities, depending on the coupling strength among successive microcavities and in some cases may remain immobile like frozen bubbles of light.

© 2004 Optical Society of America